%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:39:38 AM UTC 2026
% Result : Theorem 0.83s 1.02s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 10 unt; 0 def)
% Number of atoms : 161 ( 69 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 196 ( 81 ~; 79 |; 25 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 214 ( 200 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( X1 = X4
& X2 = vabs(X3,X0,X5) )
=> ( ( ( X3 != X4
& visFreeVar(X4,X5) )
=> visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
=> ( X3 != X4
& visFreeVar(X4,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f32,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( X2 = X1
& X3 = X0
& X4 = vabs(X6,X7,X8) )
=> ( X1 = X6
=> ( X5 = vsubst(X2,X3,X4)
=> X5 = vabs(X6,X7,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3) ).
fof(f56,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ visFreeVar(X0,X3)
& vtcheck(vbind(X0,X1,X2),X3,X4) )
=> vtcheck(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
fof(f60,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 != X4
& ~ visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2') ).
fof(f61,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 != X4
& visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-3') ).
fof(f62,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs') ).
fof(f63,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f64,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(ennf_transformation,[],[f63]) ).
fof(f65,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(flattening,[],[f64]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( X5 = vabs(X6,X7,X8)
| vsubst(X2,X3,X4) != X5
| X1 != X6
| X1 != X2
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(ennf_transformation,[],[f32]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( X5 = vabs(X6,X7,X8)
| vsubst(X2,X3,X4) != X5
| X1 != X6
| X1 != X2
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(flattening,[],[f76]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| ~ visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(ennf_transformation,[],[f61]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| ~ visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(ennf_transformation,[],[f60]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(flattening,[],[f82]) ).
fof(f90,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| visFreeVar(X0,X3)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(ennf_transformation,[],[f56]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| visFreeVar(X0,X3)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(flattening,[],[f90]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( visFreeVar(X1,X2)
| X3 = X4
| ~ visFreeVar(X4,X5) )
& ( ( X3 != X4
& visFreeVar(X4,X5) )
| ~ visFreeVar(X1,X2) ) )
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(ennf_transformation,[],[f11]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( visFreeVar(X1,X2)
| X3 = X4
| ~ visFreeVar(X4,X5) )
& ( ( X3 != X4
& visFreeVar(X4,X5) )
| ~ visFreeVar(X1,X2) ) )
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(flattening,[],[f96]) ).
fof(f105,plain,
( ~ vtcheck(sK1,vsubst(sK2,sK3,vabs(sK4,sK5,veabs)),sK6)
& vtcheck(sK1,sK3,sK0)
& vtcheck(vbind(sK2,sK0,sK1),vabs(sK4,sK5,veabs),sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f65]) ).
fof(f106,plain,
vtcheck(vbind(sK2,sK0,sK1),vabs(sK4,sK5,veabs),sK6),
inference(cnf_transformation,[],[f105]) ).
fof(f107,plain,
vtcheck(sK1,sK3,sK0),
inference(cnf_transformation,[],[f105]) ).
fof(f108,plain,
~ vtcheck(sK1,vsubst(sK2,sK3,vabs(sK4,sK5,veabs)),sK6),
inference(cnf_transformation,[],[f105]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vabs(X6,X7,X8) = X5
| vsubst(X2,X3,X4) != X5
| X1 != X6
| X1 != X2
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(cnf_transformation,[],[f77]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| ~ visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(cnf_transformation,[],[f83]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3)
| vtcheck(X2,X3,X4) ),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4] :
( vsubst(X2,X3,X4) = vabs(X6,X7,X8)
| X1 != X6
| X1 != X2
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(equality_resolution,[],[f120]) ).
fof(f155,plain,
! [X2,X3,X0,X8,X6,X7,X4] :
( vsubst(X2,X3,X4) = vabs(X6,X7,X8)
| X2 != X6
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(equality_resolution,[],[f154]) ).
fof(f156,plain,
! [X3,X0,X8,X6,X7,X4] :
( vabs(X6,X7,X8) = vsubst(X6,X3,X4)
| X0 != X3
| vabs(X6,X7,X8) != X4 ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X3,X8,X6,X7,X4] :
( vabs(X6,X7,X8) = vsubst(X6,X3,X4)
| vabs(X6,X7,X8) != X4 ),
inference(equality_resolution,[],[f156]) ).
fof(f158,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f157]) ).
fof(f177,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| X1 != X4
| vabs(X4,X0,X5) != X2 ),
inference(equality_resolution,[],[f136]) ).
fof(f178,plain,
! [X2,X0,X4,X5] :
( ~ visFreeVar(X4,X2)
| vabs(X4,X0,X5) != X2 ),
inference(equality_resolution,[],[f177]) ).
fof(f179,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f178]) ).
fof(f211,plain,
( vtcheck(sK1,vabs(sK4,sK5,veabs),sK6)
| visFreeVar(sK2,vabs(sK4,sK5,veabs)) ),
inference(resolution,[],[f130,f106]) ).
fof(f328,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| X2 = X4
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(forward_subsumption_resolution,[],[f123,f122]) ).
fof(f329,plain,
! [X0] :
( ~ vtcheck(vbind(sK2,X0,sK1),vabs(sK4,sK5,veabs),sK6)
| ~ vtcheck(sK1,sK3,X0)
| sK2 = sK4 ),
inference(resolution,[],[f328,f108]) ).
fof(f332,plain,
( ~ vtcheck(sK1,sK3,sK0)
| sK2 = sK4 ),
inference(resolution,[],[f329,f106]) ).
fof(f335,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f332,f107]) ).
fof(f372,plain,
~ vtcheck(sK1,vsubst(sK2,sK3,vabs(sK2,sK5,veabs)),sK6),
inference(superposition,[],[f108,f335]) ).
fof(f373,plain,
( vtcheck(sK1,vabs(sK2,sK5,veabs),sK6)
| visFreeVar(sK2,vabs(sK2,sK5,veabs)) ),
inference(superposition,[],[f211,f335]) ).
fof(f374,plain,
vtcheck(sK1,vabs(sK2,sK5,veabs),sK6),
inference(forward_subsumption_resolution,[],[f373,f179]) ).
fof(f375,plain,
~ vtcheck(sK1,vabs(sK2,sK5,veabs),sK6),
inference(forward_demodulation,[],[f372,f158]) ).
fof(f387,plain,
$false,
inference(forward_subsumption_resolution,[],[f375,f374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:55:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/1.02 % (1228399)Detected formulas, will run a generic FOF schedule.
% 0.83/1.02 % (1228408)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1337587041:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.83/1.02 % (1228408)First to succeed.
% 0.83/1.02 % (1228408)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1228399"
% 0.83/1.02 % (1228406)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3305187506:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.83/1.02 % (1228404)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2091869226:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.83/1.02 % (1228405)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2817116826:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.83/1.02 % (1228407)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=726292605:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.83/1.02 % (1228407)Also succeeded, but the first one will report.
% 0.83/1.02 % (1228409)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3656281537:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.83/1.02 % (1228410)dis-21_1_sil=8000:lcm=predicate:random_seed=3184554276:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.83/1.02 % (1228409)Also succeeded, but the first one will report.
% 0.83/1.02 % (1228410)Instruction limit reached!
% 0.83/1.02 % (1228410)------------------------------
% 0.83/1.02 % (1228410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/1.02 % (1228410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/1.02 % (1228410)CaDiCaL version: 2.1.3
% 0.83/1.02 % (1228410)Termination reason: Instruction limit
% 0.83/1.02 % (1228410)Termination phase: Saturation
% 0.83/1.02 % (1228410)Time elapsed: 0.075 s
% 0.83/1.02 % (1228410)Peak memory usage: 90 MB
% 0.83/1.02 % (1228410)Instructions burned: 130 (million)
% 0.83/1.02 % (1228408)Refutation found. Thanks to Tanya!
% 0.83/1.02 % SZS status Theorem for theBenchmark
% 0.83/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/1.02 % (1228408)------------------------------
% 0.83/1.02 % (1228408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/1.02 % (1228408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/1.02 % (1228408)CaDiCaL version: 2.1.3
% 0.83/1.02 % (1228408)Termination reason: Refutation
% 0.83/1.02 % (1228408)Time elapsed: 0.006 s
% 0.83/1.02 % (1228408)Peak memory usage: 89 MB
% 0.83/1.02 % (1228408)Instructions burned: 14 (million)
% 0.83/1.02 % (1228408)------------------------------
% 0.83/1.02 % (1228408)------------------------------
% 0.83/1.02 % (1228399)Success in time 0.275 s
% 0.83/1.02 % Vampire exiting
%------------------------------------------------------------------------------